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Course: Differential Geometry Instructor: Aniruddha Naolekar Room: G23 Level: Undergraduate Time: Currently offered
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Syllabus Past Exams Syllabus:
Curves in two and three dimensions, Curvature and torsion for space curves, Existence theorem for space curves, Serret-Frenet formula for space curves, Inverse and implicit function
theorems, Jacobian theorem, Surfaces in R^3 as two dimensional manifolds, Tangent space and derivative of maps between manifolds, First fundamental form, Orientation of a surface, Second
fundamental form and the Gauss map, Mean curvature and scalar curvature, Integration onsurfaces, Stokes formula, Gauss-Bonnet theorem.Reference Texts:1. M.P. do Carmo: Differential Geometry of Curves and Surfaces. 2. A. Pressley: Elementary Differential Geometry. 3. J. A. Thorpe: Introduction to Elementary Differential Geometry. Evaluation:
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Midterm
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